Post on 24-Nov-2015
description
0MC2010: The Critical Shear Crack Theory as a mechanical
model for punching shear design and itsapplication to code provisions
Prof. Dr Aurelio Muttoni
Dr Miguel Fernndez Ruiz
cole Polytechnique Fdrale de Lausanne, Switzerland
1Load test 1909
Claude A. P. Turner (1869 1955)
Load test 1908
Robert Maillart (1872-1940)
Introduction
2Introduction
3Geneva, Switzerland, 1976
Bluche, Switzerland, 1981
Wolverhampton, UK, 1997
Cagliari, Italy, 2004
Introduction
4Introduction
Design based on empirical formulas without taking into account size-effect
No shear reinforcement, no integrity reinforcement
Brittleness
Gretzenbach, Switzerland, 2004
5Introduction
Jonen, Switzerland, 2007
(Photo courtesy HALFEN AG, Switzerland)
Need for a mechanical model for slabs without and with shear reinforcement
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%
200%
0% 100% 200% 300% 400%
Deformation capacityF
orc
e
Without punching shear reinforcement
With punching shear
reinforcement
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%
200%
0% 100% 200% 300% 400%
Deformation capacityF
orc
e
Without punching shear reinforcement
With punching shear
reinforcement
6Introduction
1. Development of a mechanical model: the Critical Shear Crack Theory
2. Extensive validation by testing
7The CSCT: experimental verification in Lausanne
28
102
73 1
0
20
40
60
80
100
120
125 250 320 400 500
Thickness [mm]
Nu
mb
er o
f te
sts
8The CSCT: experimental verification in Lausanne
28
102
73 1
0
20
40
60
80
100
120
125 250 320 400 500
Thickness [mm]
Nu
mb
er o
f te
sts
9The CSCT: experimental verification in Lausanne
28
102
73 1
0
20
40
60
80
100
120
125 250 320 400 500
Thickness [mm]
Nu
mb
er o
f te
sts
10
The CSCT: experimental verification in Lausanne
28
102
73 1
0
20
40
60
80
100
120
125 250 320 400 500
Thickness [mm]
Nu
mb
er o
f te
sts
11
The CSCT: experimental verification in Lausanne
28
102
73 1
0
20
40
60
80
100
120
125 250 320 400 500
Thickness [mm]
Nu
mb
er o
f te
sts
Total #: 141 tests
12
Fundamentals of the CSCT
y
Walraven J.C. 1981, Fundamental Analysis of Aggregate Interlock, Journal of the Structural Division, Vol. 107, No. 11, pp. 2245 2270.
extreme parameters
13
Fundamentals of the CSCT
Muttoni A., 2008, Punching shear strength of reinforced concrete slabs without transverse reinforcement, ACI Structural Journal, V. 105, No 4, pp. 440-450
theoretical model based on aggregate interlock
simplified failure criterion
14
Fundamentals of the CSCT: punching shear design
Average
Characteristic
Muttoni A., 2008, Punching shear strength of reinforced concrete slabs without transverse reinforcement, ACI Structural Journal, V. 105, No 4, pp. 440-450
Load-rotation curve
Failure criterionyR
VR
15
Physical model: application to non-symmetrical cases (moment transfer)
Evaluation of w accounting for transfer moment (msd)
Shear field and shear forces along control perimeter
16
Physical model: application to non-symmetrical cases (moment transfer)
MC 2010 EC 2
17
Physical model: application to non-symmetrical cases (moment transfer)
Vocke, H, 2002, Zum Durchstanzen von Flachdecken im Bereich von Rand- und Ecksttzen, PhD. thesis, University of Stuttgart, 228 p.
18
Physical model: application to non-symmetrical cases (moment transfer)
Vocke, H, 2002, Zum Durchstanzen von Flachdecken im Bereich von Rand- und Ecksttzen, PhD. thesis, University of Stuttgart, 228 p.
19
Physical model: application to bridge deck slabs
Avg: 1.07; CoV: 13%
Vaz Rodrigues, R., Fernndez Ruiz, M., Muttoni, A., 2008, Punching shear strength of R/C bridge cantilever slabs, Engineering Structures, Elsevier, Vol. 30, No. 11, pp. 3024-3033
20
Physical model: application to shear-reinforced slabs
Fernndez Ruiz, M., Muttoni, A., 2009, Applications of the critical shear crack theory to punching of R/C slabs with transverse reinforcement, ACI Structural Journal, Vol. 106, No. 4, 2009, pp. 485-494
21
Physical model: application to shear-reinforced slabs (2nd failure mode)
22
Physical model: application to shear-reinforced slabs (2nd failure mode)
23
Physical model: application to shear-reinforced slabs
Fernndez Ruiz, M., Muttoni, A., Kunz, J., 2010, Strengthening of flat slabs against punching shear using post-installed shear reinforcement, ACI Structural Journal, Vol. 107, No. 4, pp. 434-442
24
Physical model: application to shear-reinforced slabs (3rd failure mode)
25
Physical model: application to shear-reinforced slabs
Fernndez Ruiz, M., Muttoni, A., 2009, Applications of the critical shear crack theory to punching of R/C slabs with transverse reinforcement, ACI Structural Journal, Vol. 106, No. 4, 2009, pp. 485-494
26
Physical model: retrofitting
27
Physical model: retrofitting
28
Physical model: retrofitting
29
Physical model: fibre-reinforced concrete
30
Physical model: fibre-reinforced concrete
Voo, J.Y.L. and Foster, S.J., 2004, Tensile Fracture of Fibre Reinforced Concrete: Variable Engagement Model, Sixth Rilem Symposium on Fibre Reinforced Concrete (FRC), Varenna, Italy, 20-22 September, pp. 875-884
31
Code provisions
MC-2010: 8 pages (with commentary)
32
Code provisions
MC-2010: 8 pages (with commentary)
EC-2: 10 pages
33
NMC-Calculation of Load-rotation curve: Levels-of-Approximation approach
Preliminary design
Typical design
Assessment of existing structures, design of special cases
Schertenleib P., Muttoni A., Schwartz J., 2003, Pices comprimes, Documentation SIA, D 0182 Introduction la norme SIA 262, Zrich, Switzerland, pp. 67-77
34
NMC: Levels-of-Approximation approach
Level I of approximation
http://ibeton.epfl.ch/MC2010Punching
35
NMC: Levels-of-Approximation approach
Level II of approximation
36
37
Conclusions
The CSCT is grounded on a consistent mechanical model and has been checked against extensive experimental data
The accuracy of the mechanical parameters can be progressively refined in various levels of approximation
The theory can be easily adapted to unusual cases, providing the designer with a clear understanding of the structural behaviour
The CSCT can be consistently used to investigate and to design shear-reinforced and fibre-reinforced slabs
The theory can be implemented efficiently into design codes
38
Coefficient ke
39
Influence of transfer moments
s
ididd
sdb
eVMVm
28
,
40
Fibre-reinforced concrete
41
CSCT vs. other codes (1/2)
42
CSCT vs. other codes (2/2)
43
Crushing strength (1/2)
44
Crushing strength (2/2)
45
Influence of column size
V
y
46
Slabs with punching shear reinforcement (crushing of concrete struts)
MC-90, EC-2